Question

Integral x² sin (3x-1) dx

Answer 1

Verified answer

∫ (x² - 3x + 1)sin x dx 

misal:
u = x² - 3x + 1 → du = 2x - 3 dx
dv = sin x dx   → v = -cos x

∫ (x²-3x+1)sin x dx = u.v - ∫ v.du
                             = (x²-3x+1)(-cos x) - ∫ (-cos x)(2x-3) dx
                             = -(x²-3x+1)(cos x) + ∫ (cos x)(2x-3) dx
misal:
        u = 2x-3  → du = 2 dx
 dv = cos x dx → v = sin x                          

-(x²-3x+1)(cos x) + ∫ (cos x)(2x-3) dx
= -(x²-3x+1)(cos x) + (2x-3)sin x - ∫ 2sin x
= -(x²-3x+1)(cos x) + (2x-3)sin x + 2cos x + C
= -(x²-3x-1)(cos x) + (2x-3)sin x + C
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jadikan sebagai jawaban yg terbaiik ya^__^